In Exercises 55–56, write the system of linear equations for which Cramer's Rule yields the given determinants. 2 - 4 8 - 4D = D_x = 3 5 - 10 5

Cramer's Rule is a mathematical theorem used to solve systems of linear equations with as many equations as unknowns, using determinants. It states that the solution for each variable can be found by taking the ratio of the determinant of a modified matrix (where the column corresponding to the variable is replaced by the constants from the equations) to the determinant of the coefficient matrix.

A determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties of the matrix, such as whether it is invertible. For a 2x2 matrix, the determinant is calculated as ad - bc, where the matrix is represented as [[a, b], [c, d]]. Determinants are crucial in Cramer's Rule for determining the solutions of linear systems.

A system of linear equations is a collection of two or more linear equations involving the same set of variables. The solution to the system is the set of values that satisfy all equations simultaneously. In the context of Cramer's Rule, the system can be represented in matrix form, where the coefficients of the variables form the coefficient matrix, and the constants form the constant matrix.